Collimating lenses from non-Euclidean transformation optics

Based on the non-Euclidean transformation optics, we design a thin metamaterial lens that can achieve wide-beam radiation by embedding a simple source (a point source in three-dimensional case or a line current source in two-dimensional case). The scheme is performed on a layer-by-layer geometry to convert curved surfaces in virtual space to flat sheets, which pile up and form the entire lens in physical space. Compared to previous designs, the lens has no extreme material parameters. Simulation results confirm its functionality.Comment: 12 pages, 6 figure

Perfect imaging: they don't do it with mirrors

Imaging with a spherical mirror in empty space is compared with the case when the mirror is filled with the medium of Maxwell's fish eye. Exact time-dependent solutions of Maxwell's equations show that perfect imaging is not achievable with an electrical ideal mirror on its own, but with Maxwell's fish eye in the regime when it implements a curved geometry for full electromagnetic waves

Quantum levitation by left-handed metamaterials

Left-handed metamaterials make perfect lenses that image classical electromagnetic fields with significantly higher resolution than the diffraction limit. Here we consider the quantum physics of such devices. We show that the Casimir force of two conducting plates may turn from attraction to repulsion if a perfect lens is sandwiched between them. For optical left-handed metamaterials this repulsive force of the quantum vacuum may levitate ultra-thin mirrors

Quantum homodyne tomography with a priori constraints

I present a novel algorithm for reconstructing the Wigner function from homodyne statistics. The proposed method, based on maximum-likelihood estimation, is capable of compensating for detection losses in a numerically stable way.Comment: 4 pages, REVTeX, 2 figure

Operational Theory of Homodyne Detection

We discuss a balanced homodyne detection scheme with imperfect detectors in the framework of the operational approach to quantum measurement. We show that a realistic homodyne measurement is described by a family of operational observables that depends on the experimental setup, rather than a single field quadrature operator. We find an explicit form of this family, which fully characterizes the experimental device and is independent of a specific state of the measured system. We also derive operational homodyne observables for the setup with a random phase, which has been recently applied in an ultrafast measurement of the photon statistics of a pulsed diode laser. The operational formulation directly gives the relation between the detected noise and the intrinsic quantum fluctuations of the measured field. We demonstrate this on two examples: the operational uncertainty relation for the field quadratures, and the homodyne detection of suppressed fluctuations in photon statistics.Comment: 7 pages, REVTe

Distinguishing two single-mode Gaussian states by homodyne detection: An information-theoretic approach

It is known that the quantum fidelity, as a measure of the closeness of two quantum states, is operationally equivalent to the minimal overlap of the probability distributions of the two states over all possible POVMs; the POVM realizing the minimum is optimal. We consider the ability of homodyne detection to distinguish two single-mode Gaussian states, and investigate to what extent it is optimal in this information-theoretic sense. We completely identify the conditions under which homodyne detection makes an optimal distinction between two single-mode Gaussian states of the same mean, and show that if the Gaussian states are pure, they are always optimally distinguished.Comment: 6 pages, 4 figures, published version with a detailed discussio

Optimal phase measurements with pure Gaussian states

We analyze the Heisenberg limit on phase estimation for Gaussian states. In the analysis, no reference to a phase operator is made. We prove that the squeezed vacuum state is the most sensitive for a given average photon number. We provide two adaptive local measurement schemes that attain the Heisenberg limit asymptotically. One of them is described by a positive operator-valued measure and its efficiency is exhaustively explored. We also study Gaussian measurement schemes based on phase quadrature measurements. We show that homodyne tomography of the appropriate quadrature attains the Heisenberg limit for large samples. This proves that this limit can be attained with local projective Von Neuman measurements.Comment: 9 pages. Revised version: two new sections added, revised conclusions. Corrected prose. Corrected reference

New intensity and visibility aspects of a double loop neutron interferometer

Various phase shifters and absorbers can be put into the arms of a double loop neutron interferometer. The mean intensity levels of the forward and diffracted beams behind an empty four plate interferometer of this type have been calculated. It is shown that the intensities in the forward and diffracted direction can be made equal using certain absorbers. In this case the interferometer can be regarded as a 50/50 beam splitter. Furthermore the visibilities of single and double loop interferometers are compared to each other by varying the transmission in the first loop using different absorbers. It can be shown that the visibility becomes exactly 1 using a phase shifter in the second loop. In this case the phase shifter in the second loop must be strongly correlated to the transmission coefficient of the absorber in the first loop. Using such a device homodyne-like measurements of very weak signals should become possible.Comment: 12 pages, 9 figures, accepted for publication in the Journal of Optics B - Quantum and Semiclassical Optic

Perfect imaging with geodesic waveguides

Transformation optics is used to prove that a spherical waveguide filled with an isotropic material with radial refractive index n=1/r has radial polarized modes (i.e. the electric field has only radial component) with the same perfect focusing properties as the Maxwell Fish-Eye lens. The approximate version of that device using a thin waveguide with a homogenous core paves the way to experimentally prove perfect imaging in the Maxwell Fish Eye lens

Entanglement of identical particles and reference phase uncertainty

We have recently introduced a measure of the bipartite entanglement of identical particles, E_P, based on the principle that entanglement should be accessible for use as a resource in quantum information processing. We show here that particle entanglement is limited by the lack of a reference phase shared by the two parties, and that the entanglement is constrained to reference-phase invariant subspaces. The super-additivity of E_P results from the fact that this constraint is weaker for combined systems. A shared reference phase can only be established by transferring particles between the parties, that is, with additional nonlocal resources. We show how this nonlocal operation can increase the particle entanglement.Comment: 8 pages, no figures. Invited talk given at EQIS'03, Kyoto, September, 2003. Minor typos corrected, 1 reference adde